All categories

2 years ago

18. Which function is the result of translating y = x^2 downward by 3 units and to the left by 4 units?

Mathematics

1 answer:

algol132 years ago

6 0

Answer:

Step-by-step explanation:

Given f(x) then f(x + k) represents a horizontal translation of f(x)

• If k > 0 then shift left by k units

• If k < 0 then shift right by k units

Here the shift is 4 units to the left, thus

y = (x + 4)²

Given f(x) then f(x) + k represents a vertical translation of f(x)

• If k > 0 then shift up by k units

• If k < 0 then shift down by k units

Here the shift is 3 units down, thus

y = (x + 4)² - 3 → C

You might be interested in

Which of the following are square roots of —8 + 8i/3? Check all that apply.

8090 [49]

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, $\sqrt{-8+8i\sqrt{3}}=(a+bi)$

$(\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2$

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = $\frac{4\sqrt{3}}{b}$

By substituting the value of a in equation (1),

$(\frac{4\sqrt{3}}{b})^2-b^2=-8$

$\frac{48}{b^2}-b^2=-8$

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = $\frac{4\sqrt{3}}{b}$

For b = ±2i,

a = $\frac{4\sqrt{3}}{\pm2i}$

= $\pm\frac{2i\sqrt{3}}{(-1)}$

= $\mp 2i\sqrt{3}$

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = $\frac{4\sqrt{3}}{\pm 2\sqrt{3}}$

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

6 0

2 years ago

Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she

Sergeeva-Olga [200]

A) .10 d + .25 q = 7.75
B) d + q = 40

Multiplying B) by -.10
B) -.10d -.10q = -4.0
Then adding this to A)
A) .10 d + .25 q = 7.75
.15q = 3.75

Quarters = 25
Therefore, dimes = 15
***************************************************
Double-Check
A) .10 d + .25 q = 7.75
A) .10 * 15 d + .25 * 25 = 7.75
A) 1.50 + 6.25 = 7.75

Correct!!

6 0

2 years ago

What is the mode of this data on the quiz scores? 100, 98, 95, 92, 88, 85, 80, 75

larisa86 [58]

Answer:

There is no mode.

Step-by-step explanation:

Be sure to put in there is no mode, don't put in zero. If you put in zero, it will seem like ) is the mode, you know what I mean.

Be sure to mark me Brainliest!

7 0

2 years ago

Daniella made gift bows from 8 yards of ribbon. The bows are all the same size. If she made 16 bows, how much ribbon did she use

solniwko [45]

Answer:

1.5 feet

Step-by-step explanation:

there are three feet in a yard, so 8*3= 24, and 24/16=1.5 feet of ribbon used for each bow

4 0

2 years ago

The area of a rectangular gymnasium is (5x+5x) square feet. If it is 5x feet wide, what is the length, in feet?

Amiraneli [1.4K]

Answer:

Step-by-step explanation:

Area = L x W gym area is (5x + 5x) ft² if W = 5x Find the L

Area = L x W divide both sides by W

Area/W = (L x W) / W

Area/W = L = Area/W

L = Area/W

= (5x + 5x) / (5x)

= 5x( 1 + 1) / 5x

= 5x(2) / 5x the 5x's cancel each other 5x/5x = 1

= 2 ft I got 2. I suspect the 12 was a typo and should have been 2

5 0

2 years ago